LQR weight self-tuning method and device for electromechanical system resonance suppression

Abstract

This invention discloses an LQR weight self-tuning method and apparatus for resonance suppression in electromechanical systems. The method includes: obtaining a discrete-time state-space model of the electromechanical system; setting performance indicators for an LQR controller based on the discrete-time state-space model; obtaining a discrete-time algebraic Riccati equation based on the performance indicators of the LQR controller; iteratively searching for the optimal weight coefficients based on the search range and search step size of the weight coefficients, using the frequency domain resonance peak difference as a criterion; calculating the optimal state feedback gain matrix based on the optimal weight coefficients and the discrete-time algebraic Riccati equation, thereby completing the LQR controller design; and connecting the LQR controller to the controlled system to form a closed-loop control system. This invention correlates frequency domain resonance characteristics with weight coefficients, achieving automatic optimization of LQR weight coefficients, completely avoiding manual trial and error, and greatly improving efficiency.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to an LQR weight self-tuning method, apparatus, terminal equipment, and computer-readable storage medium for suppressing resonance in electromechanical systems. Background Technology

[0002] Electromechanical systems, such as precision CNC machine tools, industrial robots, flexible robotic arms, and disk drives, often exhibit significant mechanical resonance characteristics due to their structural flexibility and transmission chain clearances. This characteristic creates towering "resonance peaks" and deep "anti-resonance valleys" at specific frequencies in the system's frequency response. During closed-loop control, these resonance peaks can cause severe overshoot, continuous oscillations, and even instability in the system's dynamic response, severely limiting its high-speed, high-precision, and stable operation performance. Therefore, effectively suppressing resonance is crucial for improving the overall performance of electromechanical systems.

[0003] Currently, the most direct method for suppressing resonance in engineering is to use a notch filter. However, the design effectiveness of a notch filter is highly dependent on obtaining accurate model information such as the system's resonant frequency, peak value, and bandwidth. When the system's resonant characteristics change due to temperature drift, wear, or load variations, the suppression effect of a notch filter with fixed parameters will significantly decrease, and it may even introduce additional phase hysteresis due to frequency mismatch, thus deteriorating system stability.

[0004] The Linear Quadratic Regulator (LQR), as an optimal control method based on a state-space model, designs full-state feedback by minimizing a quadratic performance index that integrates state error and control energy. Its theoretical advantage lies in providing good stability margin and robustness for the closed-loop system. Furthermore, by adjusting the weight matrix in the performance index, it is theoretically possible to shape the closed-loop pole distribution of the system, thereby achieving active damping of resonant modes. This makes LQR a promising solution for suppressing resonance in electromechanical systems.

[0005] However, the performance of LQR controllers is highly dependent on the selection of weight matrices Q and R. In practical engineering applications, especially for the specific control objective of "resonance suppression," there has been a lack of clear and systematic theoretical guidance on how to scientifically and efficiently select weight coefficients, particularly in relating frequency domain resonance characteristics (such as peak-to-valley differences) to weight values. Currently, this mainly relies on the experience of designers and repeated trial and error, a cumbersome and inefficient process that makes it difficult to guarantee optimal resonance suppression. Existing intelligent optimization tuning methods suffer from computational complexity and slow convergence. Therefore, providing a systematic method that can directly and automatically tune LQR weight coefficients based on the system's resonant frequency domain characteristics has significant theoretical and engineering value. Summary of the Invention

[0006] To address the shortcomings of the prior art, this invention provides an LQR weight self-tuning method, apparatus, terminal device, and computer-readable storage medium for suppressing resonance in electromechanical systems.

[0007] The first objective of this invention is to provide an LQR weight self-tuning method for suppressing resonance in electromechanical systems.

[0008] The second objective of this invention is to provide an LQR weighted self-tuning device for suppressing resonance in electromechanical systems.

[0009] The third objective of this invention is to provide a terminal device.

[0010] A fourth objective of this invention is to provide a computer-readable storage medium.

[0011] The fifth objective of this invention is to provide a computer program product.

[0012] The first objective of this invention can be achieved by adopting the following technical solution:

[0013] A self-tuning method for LQR weights in electromechanical systems for resonance suppression, the method comprising:

[0014] Obtain the discrete-time state-space model of the electromechanical system;

[0015] Based on the discrete-time state-space model of the electromechanical system, the performance index of the LQR controller is set; based on the performance index of the LQR controller, the discrete-time algebraic Riccati equation is obtained.

[0016] Based on the search range and search step size of the weight coefficients, and using the frequency domain resonance peak difference as the criterion, an iterative search is performed to obtain the optimal weight coefficients; the frequency domain resonance peak difference is the difference between the global maximum value and the global minimum value of the extracted amplitude-frequency characteristics.

[0017] Based on the optimal weighting coefficients and the discrete-time algebraic Riccati equation, the optimal state feedback gain matrix is ​​calculated, thus completing the LQR controller design.

[0018] Connecting the LQR controller to the controlled system forms a closed-loop control system.

[0019] Furthermore, the search range for the weighting coefficients is [ , ;

[0020] The search range and search step size based on the weight coefficients, and the iterative search using the frequency domain resonant peak difference as the criterion to obtain the optimal weight coefficients, include:

[0021] Step 1: ;

[0022] Step 2: Based on the constructed state / output weight matrix ,calculate value, Where C is the output matrix in the discrete-time state-space model;

[0023] Step 3: Based on The state feedback gain matrix is ​​obtained by using the discrete-time algebraic Riccati equations, along with the values, R, and discrete-time state-space model.

[0024] Step 4: Calculate based on the state feedback gain matrix. The frequency response of the open-loop transfer function corresponding to the value is calculated, and the global maximum value of the amplitude-frequency characteristic is extracted. and global minimum ; ;

[0025] Step 5: If If the difference between the resonance peaks is less than the set expected threshold, the iterative search stops, and the current value is set to [value missing]. As the optimal weighting coefficient, otherwise:

[0026] Step 6: Let ; This is the search step size;

[0027] like If the condition is met, return to step 2 to continue with the subsequent operations; otherwise, [then proceed]. Output as the optimal weight coefficient .

[0028] Furthermore, the open-loop transfer function is:

[0029] ;

[0030] Where z is the transformation operator, G(z) is the controlled object model, and the transfer function of the LQR controller is... F is the state feedback gain matrix, A and B are the system matrix and input matrix in the discrete-time state-space model, respectively, zI is the z-domain identity matrix, and I is the identity matrix with the same dimension as the system matrix A.

[0031] Furthermore, , .

[0032] Furthermore, the range of the desired threshold value for the resonant peak difference is 3~10dB.

[0033] Furthermore, the discrete-time algebraic Riccati equation is:

[0034] ;

[0035] ;

[0036] Where P is the positive definite solution matrix, A and B are the system matrix and input matrix in the discrete-time state-space model, respectively, Q is the state / output weight matrix, R is the control weight matrix, and F is the state feedback gain matrix.

[0037] Furthermore, the performance metrics of the LQR controller are as follows:

[0038] ;

[0039] Where x(k) is the system state vector at time k, u(k) is the control input at time k, Q is the state / output weight matrix, and R is the control weight matrix.

[0040] The second objective of this invention can be achieved by adopting the following technical solution:

[0041] An LQR weighted self-tuning device for suppressing resonance in electromechanical systems, the device comprising:

[0042] The acquisition module is used to acquire the discrete-time state-space model of the electromechanical system.

[0043] The configuration module is used to set the performance indicators of the LQR controller based on the discrete-time state-space model of the electromechanical system; and to obtain the discrete-time algebraic Riccati equation based on the performance indicators of the LQR controller.

[0044] An iterative search module is used to perform iterative search based on the search range and search step size of the weight coefficients, and with the frequency domain resonance peak difference as the criterion, to obtain the optimal weight coefficients; the frequency domain resonance peak difference is the difference between the global maximum value and the global minimum value of the extracted amplitude-frequency characteristics.

[0045] The calculation module is used to calculate the optimal state feedback gain matrix based on the optimal weight coefficients and the discrete-time algebraic Riccati equation, thereby completing the LQR controller design.

[0046] The closed-loop control module is used to connect the LQR controller to the controlled system to form a closed-loop control system.

[0047] The third objective of this invention can be achieved by adopting the following technical solution:

[0048] A terminal device includes a processor and a memory for storing a processor-executable program. When the processor executes the program stored in the memory, it implements the above-described LQR weight self-tuning method for suppressing resonance in electromechanical systems.

[0049] The fourth objective of this invention can be achieved by adopting the following technical solution:

[0050] A computer-readable storage medium storing a program that, when executed by a processor, implements the above-described LQR weight self-tuning method for suppressing resonance in electromechanical systems.

[0051] The fifth objective of this invention can be achieved by adopting the following technical solution:

[0052] A computer program product includes a computer program that, when executed by a processor, implements the aforementioned LQR weighted self-tuning method for electromechanical system resonance suppression of a motor.

[0053] The present invention has the following advantages over the prior art:

[0054] (1) Self-tuning and automation with strong resonance suppression: By using the monotonic step-by-step iterative search strategy of the weight coefficient ρ, the LQR weight coefficient is automatically optimized with the frequency domain resonance peak difference as the clear criterion. The peak-valley difference is directly used as the core optimization target, so that the tuning process revolves around the resonance suppression requirement throughout, completely avoiding manual trial and error, greatly improving design efficiency, and making the resonance suppression effect more intuitive and controllable.

[0055] (2) Clear physical meaning: weighting coefficient pass Directly related to system output, adjustment Essentially, it adjusts the penalty weights for output errors, and its relationship with frequency domain flattening is easy to understand.

[0056] (3) Computationally efficient: It adopts a monotonic step search strategy, which is simple in logic, has a small amount of computation, fast convergence speed, and is easy to implement in engineering.

[0057] (4) Good robustness: The tuning method based on frequency domain characteristics is not sensitive to a certain degree of uncertainty in the model, and LQR itself has good robustness. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0059] Figure 1 This is a flowchart of the LQR weight self-tuning method for suppressing resonance in electromechanical systems according to Embodiment 1 of the present invention;

[0060] Figure 2 This is a flowchart of the iterative search in Embodiment 1 of the present invention;

[0061] Figure 3 The following are comparison diagrams of the open-loop frequency characteristics of the system with and without the method provided in Embodiment 1 of the present invention, wherein (a) is a comparison diagram of amplitude frequency characteristics and (b) is a comparison diagram of phase frequency characteristics.

[0062] Figure 4 This is a structural block diagram of the LQR weighted self-tuning device for suppressing resonance in electromechanical systems according to Embodiment 2 of the present invention;

[0063] Figure 5 This is a structural block diagram of the terminal device according to Embodiment 3 of the present invention. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be understood that the specific embodiments described are merely used to explain this application and are not intended to limit this application.

[0065] Example 1:

[0066] like Figure 1 As shown, the LQR weight self-tuning method for suppressing resonance in electromechanical systems provided in this embodiment includes the following steps:

[0067] S101. Obtain the discrete-time state-space model of the electromechanical system.

[0068] Discrete-time state-space models can be obtained through system identification or mechanism modeling, and balancing can be performed as needed to improve numerical stability.

[0069] In one embodiment, taking a flexible electromechanical servo system as the controlled object, an example of its discrete-time state-space model describing resonance characteristics is as follows:

[0070] Equations of state:

[0071] Output equation:

[0072] Where x(k) is the system state vector at time k, u(k) is the control input at time k, y(k) is the system output at time k, and A, B, and C are the system matrix, input matrix, and output matrix, respectively, and are all known real matrices.

[0073] Specifically, the system matrix A, input matrix B, and output matrix C are as follows:

[0074]

[0075]

[0076]

[0077] In this embodiment, the system sampling period T_s is set to 0.01 seconds.

[0078] The above model will serve as the basis for the LQR controller design and automatic weight search in subsequent steps.

[0079] S102. Based on the discrete-time state-space model of the electromechanical system, set the performance index of the LQR controller; based on the performance index, obtain the discrete-time algebraic Riccati equation.

[0080] LQR state feedback design involves designing a state feedback controller. This minimizes the quadratic performance index function J, thus yielding the discrete-time algebraic Riccati equation.

[0081] The performance index function J is:

[0082]

[0083] Where Q is the state / output weight matrix and R is the control weight matrix.

[0084] The performance index function J is the core basis for the design of the LQR controller. It is directly used to solve the discrete-time algebraic Riccati equation during the iterative search process. By adjusting Q (constructed from the weight coefficient ρ) and fixing R, the state feedback gain matrix F corresponding to different ρ is obtained, which supports the subsequent construction of the open-loop system and the evaluation of the resonance suppression effect.

[0085] S103. Based on the search range and search step size of the weight coefficients, perform iterative search using the frequency domain resonant peak difference as the criterion to obtain the optimal weight coefficients.

[0086] The optimal weighting coefficients are obtained by iteratively searching based on the initial search parameters and the difference between the frequency domain resonant peaks.

[0087] Further, refer to Figure 2 Step S103 includes:

[0088] (1) Initialize search parameters.

[0089] The search parameters include: the scalar weight coefficients to be tuned. Minimum and maximum weight coefficients , and search step size Expected threshold for difference between resonance peak and resonance peak .

[0090] in, , The value range is 3~10dB.

[0091] In this embodiment, based on prior knowledge of the system, the search parameters are initialized as follows: , , , .

[0092] (2) Design an LQR controller.

[0093] The state / output weight matrix is ​​constructed using an output-weighted approach. , .

[0094] The state feedback gain matrix F is obtained by solving the following discrete-time algebraic Riccati equation:

[0095]

[0096]

[0097] Where P is the unique positive definite solution matrix of the discrete-time algebraic Riccati equation.

[0098] (3) Construct an open-loop system.

[0099] The transfer function of the LQR controller is:

[0100]

[0101] Where zI is the z-domain identity matrix, z is the transformation operator, and I is the identity matrix with the same dimension as the system matrix A, which is the standard matrix form in the derivation of the transfer function of a discrete-time system.

[0102] Transfer function of LQR controller By concatenating it with the controlled object model G(z), the current weight coefficients are obtained. The open-loop transfer function is as follows: .

[0103] (4) Frequency domain analysis and resonance feature extraction.

[0104] Search scope Inside, calculate each one in turn. value corresponding The frequency response of the open-loop transfer function is calculated, and the global maximum value of the amplitude-frequency response is extracted. and global minimum .

[0105] The frequency response ranges from 0.01 to 50 Hz, covering the main resonant frequencies of the controlled system.

[0106] (5) Judgment based on criteria.

[0107] Calculate the absolute value of the difference between the two peaks. .

[0108] (6) Iterative decision making.

[0109] like If the search stops, the current search will be stopped. Record as the optimal weight coefficient ;otherwise:

[0110] make ;like If the condition is met, return to step (2) to continue with the subsequent operations; otherwise, [then proceed]. As the optimal weighting coefficient Output At this point, the system can still achieve a better resonance suppression effect than the original system.

[0111] S104. Based on the optimal weight coefficients and the discrete-time algebraic Riccati equation, calculate the optimal state feedback gain matrix to complete the LQR controller design.

[0112] Based on optimal weight coefficients and weight matrix ,calculate Based on Solving the Riccati equation yields the optimal state feedback gain matrix. This constitutes a complete LQR controller. .

[0113] S105. Connect the LQR controller to the controlled system to form a closed-loop control system.

[0114] The controller It is placed in the forward channel and forms a unit negative feedback closed-loop control system with the controlled object.

[0115] Figure 3The amplitude-frequency response curve in (a) shows that the original controlled object has a significant resonant peak near 14Hz and an anti-resonant valley near 10Hz, with a huge difference between the peak and valley. This strong resonant characteristic can easily cause overshoot, oscillation, or even instability in actual operation. After adaptive LQR control in this embodiment, the resonant peak is effectively suppressed, and the anti-resonant valley is raised, successfully reducing the difference between the resonant peak and the anti-resonant peak from 37.18dB in the original system to less than 5dB, achieving the preset control target and making the entire amplitude-frequency curve flatter. This means that the gain fluctuation of the system near the resonant frequency is significantly reduced, thereby directly reducing the risk of overshoot and oscillation caused by resonance and improving the dynamic stability of the system.

[0116] Figure 3 The phase-frequency response curve in (b) also shows that the phase characteristics of the system are improved and the phase margin is increased. The increase in phase margin further enhances the stability and robustness of the system, making the system more resistant to model uncertainties and external disturbances.

[0117] The above experiments demonstrate that this embodiment automatically searches for suitable... This not only achieves effective resonance suppression based on the resonance peak difference criterion, but also comprehensively improves the dynamic performance, stability and robustness of the system.

[0118] In another embodiment, the LQR weighted self-tuning method for electromechanical system resonance suppression provided in the above embodiments is also applicable to different controlled objects. During implementation, only the search parameters in step S103 need to be adjusted. , , Sum and difference thresholds This is to adapt to the dynamic characteristics and performance requirements of different objects. For example, for systems with more intense resonance, the appropriate increase can be made. For situations requiring stricter suppression, the amount of [something] can be reduced. The core search process (see reference) Figure 2 The criteria remain unchanged.

[0119] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium.

[0120] It should be noted that although the method operations of the above embodiments are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. On the contrary, the order of execution of the described steps may be changed. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0121] Example 2:

[0122] like Figure 4 As shown, this embodiment provides an LQR weight self-tuning device for suppressing resonance in electromechanical systems. The device includes an acquisition module 401, a setting module 402, an iterative search module 403, a calculation module 404, and a closed-loop control module 405, wherein:

[0123] The acquisition module 401 is used to acquire the discrete-time state-space model of the electromechanical system;

[0124] The configuration module 402 is used to set the performance index of the LQR controller based on the discrete-time state-space model of the electromechanical system; and to obtain the discrete-time algebraic Riccati equation based on the performance index of the LQR controller.

[0125] The iterative search module 403 is used to perform iterative search based on the search range and search step size of the weight coefficients, and with the frequency domain resonance peak difference as the criterion, to obtain the optimal weight coefficients; the frequency domain resonance peak difference is the difference between the global maximum value and the global minimum value of the extracted amplitude-frequency characteristics.

[0126] The calculation module 404 is used to calculate the optimal state feedback gain matrix based on the optimal weight coefficients and the discrete-time algebraic Riccati equation, thereby completing the LQR controller design.

[0127] The closed-loop control module 405 is used to connect the LQR controller to the controlled system to form a closed-loop control system.

[0128] The specific implementation of each module in this embodiment can be found in Embodiment 1 above, and will not be repeated here. It should be noted that the device provided in this embodiment is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above.

[0129] Example 3:

[0130] This embodiment provides a terminal device, which can be a computer, such as... Figure 5As shown, the processor 502, memory, input device 503, display 504, and network interface 505 are connected via system bus 501. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium 506 and internal memory 507. The non-volatile storage medium 506 stores the operating system, computer programs, and database. The internal memory 507 provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. When the processor 502 executes the computer program stored in the memory, it implements the LQR weight self-tuning method for electromechanical system resonance suppression described in Embodiment 1 above, as follows:

[0131] Obtain the discrete-time state-space model of the electromechanical system;

[0132] Based on the discrete-time state-space model of the electromechanical system, the performance index of the LQR controller is set; based on the performance index of the LQR controller, the discrete-time algebraic Riccati equation is obtained.

[0133] Based on the search range and search step size of the weight coefficients, and using the frequency domain resonance peak difference as the criterion, an iterative search is performed to obtain the optimal weight coefficients; the frequency domain resonance peak difference is the difference between the global maximum value and the global minimum value of the extracted amplitude-frequency characteristics.

[0134] Based on the optimal weighting coefficients and the discrete-time algebraic Riccati equation, the optimal state feedback gain matrix is ​​calculated, thus completing the LQR controller design.

[0135] Connecting the LQR controller to the controlled system forms a closed-loop control system.

[0136] Example 4:

[0137] This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the LQR weight self-tuning method for electromechanical system resonance suppression described in Embodiment 1 above, as follows:

[0138] Obtain the discrete-time state-space model of the electromechanical system;

[0139] Based on the discrete-time state-space model of the electromechanical system, the performance index of the LQR controller is set; based on the performance index of the LQR controller, the discrete-time algebraic Riccati equation is obtained.

[0140] Based on the search range and search step size of the weight coefficients, and using the frequency domain resonance peak difference as the criterion, an iterative search is performed to obtain the optimal weight coefficients; the frequency domain resonance peak difference is the difference between the global maximum value and the global minimum value of the extracted amplitude-frequency characteristics.

[0141] Based on the optimal weighting coefficients and the discrete-time algebraic Riccati equation, the optimal state feedback gain matrix is ​​calculated, thus completing the LQR controller design.

[0142] Connecting the LQR controller to the controlled system forms a closed-loop control system.

[0143] It should be noted that the computer-readable storage medium in this embodiment can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0144] Example 5:

[0145] This embodiment provides a computer program product, including a computer program that, when executed by a processor, implements the LQR weight self-tuning method for electromechanical system resonance suppression described in Embodiment 1 above:

[0146] Obtain the discrete-time state-space model of the electromechanical system;

[0147] Based on the discrete-time state-space model of the electromechanical system, the performance index of the LQR controller is set; based on the performance index of the LQR controller, the discrete-time algebraic Riccati equation is obtained.

[0148] Based on the search range and search step size of the weight coefficients, and using the frequency domain resonance peak difference as the criterion, an iterative search is performed to obtain the optimal weight coefficients; the frequency domain resonance peak difference is the difference between the global maximum value and the global minimum value of the extracted amplitude-frequency characteristics.

[0149] Based on the optimal weighting coefficients and the discrete-time algebraic Riccati equation, the optimal state feedback gain matrix is ​​calculated, thus completing the LQR controller design.

[0150] Connecting the LQR controller to the controlled system forms a closed-loop control system.

[0151] In summary, the LQR weight self-tuning method and system for resonance suppression in electromechanical systems provided by this invention establishes a correlation between the amplitude difference between the resonant peak and the anti-resonant peak in the system's open-loop frequency response and the LQR weight coefficients. This difference is used as a performance criterion to automatically iteratively search for the optimal weight coefficients, making the system's open-loop amplitude-frequency characteristics tend to flatten, thereby achieving efficient and adaptive resonance suppression. This invention uses the difference between the system's frequency domain resonant peaks and valleys as the core tuning criterion for the LQR weight coefficients, achieving a direct correlation with the weight coefficients. This enables automated and targeted design of the LQR controller weights, solving the problems of traditional methods relying on empirical trial and error, notch filters relying on precise models, and insufficient resonance suppression effects.

[0152] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and inventive concept of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A self-tuning method for LQR weights in electromechanical systems for resonance suppression, characterized in that, The method includes: Obtain the discrete-time state-space model of the electromechanical system; Based on the discrete-time state-space model of the electromechanical system, the performance index of the LQR controller is set; based on the performance index of the LQR controller, the discrete-time algebraic Riccati equation is obtained. Based on the search range and search step size of the weight coefficients, and using the frequency domain resonance peak difference as the criterion, an iterative search is performed to obtain the optimal weight coefficients; the frequency domain resonance peak difference is the difference between the global maximum value and the global minimum value of the extracted amplitude-frequency characteristics. Based on the optimal weighting coefficients and the discrete-time algebraic Riccati equation, the optimal state feedback gain matrix is ​​calculated, thus completing the LQR controller design. Connecting the LQR controller to the controlled system forms a closed-loop control system.

2. The LQR weight self-tuning method according to claim 1, characterized in that, The search range for the weighting coefficients is [ , ; The search range and search step size based on the weight coefficients, and the iterative search using the frequency domain resonant peak difference as the criterion to obtain the optimal weight coefficients, include: Step 1: ; Step 2: Based on the constructed state / output weight matrix ,calculate value, Where C is the output matrix in the discrete-time state-space model; Step 3: Based on The state feedback gain matrix is ​​obtained by using the discrete-time algebraic Riccati equations, along with the values, R, and discrete-time state-space model. Step 4: Calculate based on the state feedback gain matrix. The frequency response of the open-loop transfer function corresponding to the value is calculated, and the global maximum value of the amplitude-frequency characteristic is extracted. and global minimum ; ; Step 5: If If the difference between the resonance peaks is less than the set expected threshold, the iterative search stops, and the current value is set to [value missing]. As the optimal weighting coefficient, otherwise: Step 6: Let ; This is the search step size; like If the condition is met, return to step 2 to continue with the subsequent operations; otherwise, [then proceed]. Output as the optimal weight coefficient .

3. The LQR weight self-tuning method according to claim 2, characterized in that, The open-loop transfer function is: ； Where z is the transformation operator, G(z) is the controlled object model, and the transfer function of the LQR controller is... F is the state feedback gain matrix, A and B are the system matrix and input matrix in the discrete-time state-space model, respectively, zI is the z-domain identity matrix, and I is the identity matrix with the same dimension as the system matrix A.

4. The LQR weight self-tuning method according to claim 2, characterized in that, 。 5. The LQR weight self-tuning method according to claim 2, characterized in that, The desired threshold value for the resonant peak difference is set to be in the range of 3~10dB.

6. The LQR weight self-tuning method according to any one of claims 1 to 5, characterized in that, The discrete-time algebraic Riccati equation is: ； ； Where P is the positive definite solution matrix, A and B are the system matrix and input matrix in the discrete-time state-space model, respectively, Q is the state / output weight matrix, R is the control weight matrix, and F is the state feedback gain matrix.

7. The LQR weight self-tuning method according to any one of claims 1 to 5, characterized in that, The performance metrics of the LQR controller are as follows: ； Where x(k) is the system state vector at time k, u(k) is the control input at time k, Q is the state / output weight matrix, and R is the control weight matrix.

8. An LQR weighted self-tuning device for suppressing resonance in electromechanical systems, characterized in that, The device includes: The acquisition module is used to acquire the discrete-time state-space model of the electromechanical system. The configuration module is used to set the performance indicators of the LQR controller based on the discrete-time state-space model of the electromechanical system; and to obtain the discrete-time algebraic Riccati equation based on the performance indicators of the LQR controller. An iterative search module is used to perform iterative search based on the search range and search step size of the weight coefficients, and with the frequency domain resonance peak difference as the criterion, to obtain the optimal weight coefficients; the frequency domain resonance peak difference is the difference between the global maximum value and the global minimum value of the extracted amplitude-frequency characteristics. The calculation module is used to calculate the optimal state feedback gain matrix based on the optimal weight coefficients and the discrete-time algebraic Riccati equation, thereby completing the LQR controller design. The closed-loop control module is used to connect the LQR controller to the controlled system to form a closed-loop control system.

9. A terminal device, comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the LQR weight self-tuning method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the LQR weight self-tuning method according to any one of claims 1 to 7.

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